Greenpeace slams Israeli charge of Iranian eco-terror
"It is simply scandalous and lacking any factual basis at this stage," he told public radio.
He said her accusation against Israel's arch foe carried "a bad smell of election propaganda" as a March 23 general election beckons.
Gamliel is a staunch ally of Prime Minister Benjamin Netanyahu, whose hardline stance against Iran is a key part of his re-election campaign.
Aikhenbaum said her Wednesday accusations on Twitter were "a blow to Israel's credibility in the international arena and especially the credibility of the ministry for environmental protection".
Storms last month washed tonnes of sticky tar ashore along Israel's entire Mediterranean coastline, blighting 160 kilometres (96 miles) of beach from the Gaza border to Lebanon.
"Our long arm will reach anyone who harms our nature, our sea or our coasts," she warned.
Public radio has reported that the intelligence community do not share the minister's assessment.
Greenpeace said that the culprit could have been another of the vessels that were in the area at the time.
"The minister downplays the well-known and widespread phenomenon of destructive sea pollution from oil spills by ships," its website said.
Gamliel's statements came after the Jewish state accused Iran of an attack late last month on an Israeli-owned ship in the Gulf of Oman, further raising tensions.
Iran has denied any role in the explosion that hit the MV Helios Ray, leaving two holes in its side but causing no casualties.
The latest escalation between the arch rivals comes as the international community tries to salvage a troubled 2015 nuclear deal with Iran.